Network Meta-analysis with MARS — network

Fits a network meta-analysis using mars in either multilevel or multivariate mode and returns direct, indirect, and total treatment effects. Multilevel models always use flexible heterogeneity across random levels. Multivariate models can use either common or flexible heterogeneity. The "wls" model type provides a common-effect weighted least-squares compatibility estimator for comparisons against graph-theoretical network meta-analysis implementations.

Usage

network_meta(
  data,
  study_id,
  treatment_1,
  treatment_2,
  effect,
  variance,
  reference = NULL,
  model_type = c("multilevel", "multivariate", "wls"),
  heterogeneity = NULL,
  tau_components = c("comparison", "treatment"),
  nested_levels = NULL,
  moderators = NULL,
  estimation_method = "REML",
  varcov_type = "multilevel",
  within_varcov_type = NULL,
  sample_size = NULL,
  robustID = NULL,
  tau2 = NULL,
  control = list(),
  ci_level = 0.95,
  optim_method = "L-BFGS-B",
  tol = 1e+07,
  ...
)

Arguments

data: A data frame with one row per observed treatment contrast.
study_id: Character string naming the study ID column.
treatment_1: Character string naming the first treatment column.
treatment_2: Character string naming the second treatment column.
effect: Character string naming the effect-size column, interpreted as treatment_2 minus treatment_1.
variance: Character string naming the sampling-variance column.
reference: Optional treatment label to use as network reference. If NULL, the first treatment in sorted order is used.
model_type: One of "multilevel", "multivariate", or "wls".
heterogeneity: For model_type = "multilevel", must be "flexible". For model_type = "multivariate", choose "common" or "flexible".
tau_components: For model_type = "multilevel", choose "comparison" (default) or "treatment" random components.
nested_levels: Optional character vector of additional column names to append after study_id/component_id in the multilevel random-effects nesting.
moderators: Optional moderators to include in both model types. Either a one-sided formula (e.g., ~ age + risk) or a character vector of column names.
estimation_method: Estimation method passed to mars.
varcov_type: Variance-covariance type passed to mars.
within_varcov_type: For model_type = "multivariate", optional override for within-study covariance estimation used in estimation. Defaults to varcov_type when not provided.
sample_size: Optional sample-size column for multivariate mode.
robustID: Optional cluster column name for cluster-robust standard errors (for example, study ID) in model_type = "multivariate".
tau2: Optional user-supplied between-study variance or covariance passed to mars/estimation. For multilevel network models, supply one value per random-effect component. For multivariate common heterogeneity, supply one value; for flexible diagonal heterogeneity, supply one value per comparison; or supply a positive semidefinite covariance matrix to use an unstructured multivariate heterogeneity covariance.
control: Optional named list of speed diagnostics controls. Supported entries are use_sparse, reuse_inverses, parallel, and singular_threshold.
ci_level: Confidence level for normal-approximation confidence intervals returned for direct, indirect, and total effects. Defaults to 0.95.
optim_method: Optimization method passed to mars.
tol: Optimization tolerance passed to mars.
...: Additional arguments passed to mars.

Value

A list with class nma_mars containing fitted model output, direct/indirect/total effects, incoherence-factor summaries, contribution decomposition summaries, node-splitting summaries, design inconsistency diagnostics, ranking outputs, and model-fit statistics.

Examples

# \donttest{
nma_dat <- data.frame(
  study = c("S1", "S2", "S3", "S4"),
  treatment_1 = c("A", "A", "B", "A"),
  treatment_2 = c("B", "C", "C", "B"),
  effect = c(0.20, 0.35, 0.10, 0.15),
  variance = c(0.04, 0.05, 0.04, 0.06)
)
nma_fit <- network_meta(
  nma_dat,
  study_id = "study",
  treatment_1 = "treatment_1",
  treatment_2 = "treatment_2",
  effect = "effect",
  variance = "variance",
  model_type = "wls"
)
summary(nma_fit)
#> Network Meta-analysis (MARS)
#> Model Type: wls 
#> Heterogeneity: common 
#> Reference: A 
#> Treatments: A, B, C 
#> 
#> Evidence Summary:
#> $n_comparisons_total
#> [1] 3
#> 
#> $n_comparisons_with_direct
#> [1] 3
#> 
#> $n_comparisons_with_indirect
#> [1] 3
#> 
#> $n_comparisons_indirect_only
#> [1] 0
#> 
#> $n_direct_effects
#> [1] 4
#> 
#> $n_indirect_effects
#> [1] 8
#> 
#> 
#> Incoherence-Factor Assessment:
#> Global test:
#>  Q_incoherence df   p_value
#>       1.593342  3 0.6609003
#> 
#> Per-comparison incoherence factors:
#>  treatment_1 treatment_2 incoherence_factor     if_se         z   p_value
#>            A           B          0.1652632 0.2587419 0.6387182 0.5230063
#>            A           C          0.3807018 0.3578689 1.0638022 0.2874183
#>            B           C          0.0754386 0.3255225 0.2317462 0.8167352
#>    ci_lower ci_upper
#>  -0.3418616 0.672388
#>  -0.3207085 1.082112
#>  -0.5625738 0.713451
#> 
#> Contribution Matrix (% information from direct comparisons):
#>        A vs B A vs C B vs C
#> A vs B  92.87   3.17   3.96
#> A vs C  41.90  32.95  25.14
#> B vs C  28.30  13.58  58.12
#> 
#> Model Fixed Effects (SE fallback applied when needed):
#>  term  estimate std_error  z_value    p_value se_source
#>   d_B 0.1947368 0.1376494 1.414730 0.15714757   hessian
#>   d_C 0.3192982 0.1675416 1.905785 0.05667807   hessian
#> 
#> Fit Statistics:
#>  model_type heterogeneity n_treatments n_edges estimator         QE QE_df
#>        <NA>          <NA>            3       3       WLS 0.06798246     2
#>     QE_p   logLik       Dev        AIC       BIC    AICc
#>  0.96658 2.413702 -4.827404 -0.8274039 -2.054815 11.1726
#> 
#> Node-Splitting Assessment:
#>  Q_node_split df   p_value
#>      1.593342  3 0.6609003
#> 
#>  treatment_1 treatment_2 direct    indirect direct_indirect_diff   diff_se
#>            A           B   0.18  0.01473684            0.1652632 0.2587419
#>            A           C   0.35 -0.03070175            0.3807018 0.3578689
#>            B           C   0.10  0.02456140            0.0754386 0.3255225
#>          z   p_value   ci_lower ci_upper
#>  0.6387182 0.5230063 -0.3418616 0.672388
#>  1.0638022 0.2874183 -0.3207085 1.082112
#>  0.2317462 0.8167352 -0.5625738 0.713451
#> 
#> Treatment Ranking:
#>  treatment mean_effect std_error mean_rank median_rank  sucra sucr_a  p_best
#>          C   0.3192982 0.1675416    1.2375           1 88.125 88.125 0.78100
#>          B   0.1947368 0.1376494    1.8640           2 56.800 56.800 0.21325
#>          A   0.0000000 0.0000000    2.8985           3  5.075  5.075 0.00575
#> 
#> Contribution Decomposition (top rows):
#> Fixed-Effect Design Diagnostics:
#> $rank
#> [1] 2
#> 
#> $ncol
#> [1] 2
#> 
#> $condition_number
#> [1] 2.906201
#> 
#> $info_condition_number
#> [1] 1.5
#> 
#> $singular
#> [1] FALSE
#> 
#> $near_singular
#> [1] FALSE
#> 
#> $recommendation
#> [1] "No major fixed-effect rank/conditioning issues detected."
#> 
#> 
#> Treatment Order:
#>  rank treatment effect_vs_reference
#>     1         C              0.3193
#>     2         B              0.1947
#>     3         A              0.0000
#> 
#> Direct / Indirect / Total Effects:
#>  treatment_1 treatment_2 direct direct_se direct_n_studies direct_n_effects
#>            A           B   0.18    0.1549                2                2
#>            A           C   0.35    0.2236                1                1
#>            B           C   0.10    0.2000                1                1
#>  direct_observed direct_observed_se indirect indirect_se indirect_n_paths
#>             0.18             0.1549   0.0147      0.2072                1
#>             0.35             0.2236  -0.0307      0.2794                1
#>             0.10             0.2000   0.0246      0.2568                1
#>  indirect_n_studies indirect_n_effects  total total_se total_n_studies
#>                   2                  2 0.1947   0.1376               4
#>                   3                  3 0.3193   0.1675               4
#>                   3                  3 0.1246   0.1611               4
#>  total_n_effects direct_ci_lower direct_ci_upper direct_observed_ci_lower
#>                4         -0.1236          0.4836                  -0.1236
#>                4         -0.0883          0.7883                  -0.0883
#>                4         -0.2920          0.4920                  -0.2920
#>  direct_observed_ci_upper indirect_ci_lower indirect_ci_upper total_ci_lower
#>                    0.4836           -0.3914            0.4209        -0.0751
#>                    0.7883           -0.5783            0.5169        -0.0091
#>                    0.4920           -0.4788            0.5280        -0.1913
#>  total_ci_upper
#>          0.4645
#>          0.6477
#>          0.4404
#> 
#> Indirect SE note:
#> Indirect SEs are approximate; for mixed direct+indirect comparisons, var(indirect) is computed as var(total) + var(direct) assuming zero covariance. 
#> 
#> Heterogeneity Summary:
#> Overall Q:
#> $value
#> [1] 0.06798246
#> 
#> $df
#> [1] 2
#> 
#> $p
#> [1] 0.96658
#> 
#> 
#> Between-study variance (tau^2):
#> [1] component tau2     
#> <0 rows> (or 0-length row.names)
#> 
# }